Randomized dual proximal gradient for large-scale distributed optimization

Notarnicola, Ivano; Notarstefano, Giuseppe

doi:10.1109/cdc.2015.7402313

Cited by 4 publications

(6 citation statements)

References 22 publications

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“…The investigation of asynchronous dual algorithms for MPC is gaining more attention recently. In [26], for example, an asynchronous dual algorithm is proposed. Compared to [26], SVR-AMA allows the use of a generic (i.e., not necessarily uniform) probability distribution and, consequently, more flexibility in the tuning phase of the algorithm.…”

Section: B Related Workmentioning

confidence: 99%

“…Compared to other asynchronous dual algorithms (see, e.g., [26]), Algorithm 5 allows one to tune and adapt (online) the probability distribution Π. This is particularly useful, for example, to give priority in the update to those subproblems whose associated dual variables vary the most between two iterations of the algorithm, as shown in the following section.…”

Section: Remarkmentioning

confidence: 99%

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SVR-AMA: An Asynchronous Alternating Minimization Algorithm With Variance Reduction for Model Predictive Control Applications

Ferranti

Jones

et al. 2019

IEEE Trans. Automat. Contr.

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This paper focuses on the design of an asynchronous dual solver suitable for model predictive control (MPC) applications. The proposed solver relies on a state-of-the-art variance reduction (VR) scheme, previously used in the context of proximal stochastic gradient methods (Prox-SVRG) and on the alternating minimization algorithm (AMA). The resultant algorithm, a stochastic AMA with VR (SVR-AMA), shows geometric convergence (in the expectation) to a suboptimal solution of the MPC problem and, compared to other state-of-the-art dual asynchronous algorithms, allows one to tune the probability of the asynchronous updates to improve the quality of the estimates. Two novel accelerated versions of the Prox-SVRG (and, by duality, of SVR-AMA) are also provided. We apply the proposed algorithm to a specific class of splitting methods, that is, the decomposition along the length of the prediction horizon. Numerical results on the longitudinal control problem of an Airbus passenger aircraft show the benefits that we can gain in terms of computation time when using our proposed solver with an adaptive probability distribution.

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Section: B Related Workmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

SVR-AMA: An Asynchronous Alternating Minimization Algorithm With Variance Reduction for Model Predictive Control Applications

Ferranti

Jones

et al. 2019

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

show abstract

“…Furthermore, for each equality constraint in Problem (13), the corresponding Lagrange multipliers have been highlighted.…”

Section: Asynchronous Mpcmentioning

confidence: 99%

“…Compared to other asynchronous dual algorithms (e.g., [13]), Algorithm 3 allows one to tune and adapt (online) the probability distribution Π. This is particularly useful, for example, to give priority in the update to those subproblems whose associated dual variables vary the most between two iterations of the algorithm, as shown in the next section.…”

Section: If We Define Ymentioning

confidence: 99%

“…The investigation of asynchronous dual algorithms for MPC is gaining more attention recently. In [13], for example, an asynchronous dual algorithm is proposed. Compared to [13], SVR-AMA allows the use of a generic (i.e., not necessarily uniform) probability distribution and, consequently, more flexibility in the tuning phase of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Asynchronous splitting design for Model Predictive Control

Ferranti

Jones

et al. 2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-This paper focuses on the design of an asynchronous dual solver suitable for embedded model predictive control (MPC) applications. The proposed solver relies on a state-of-the-art variance reduction (VR) scheme, previously used in the context of stochastic proximal gradient methods, and on the alternating minimization algorithm (AMA). The resultant algorithm, a stochastic AMA with VR, shows geometric convergence (in the expectation) to a suboptimal solution of the MPC problem and, compared to other state-of-the-art dual asynchronous algorithms, allows to tune the probability of the asynchronous updates to improve the quality of the estimates. We apply the proposed algorithm to a specific class of splitting methods, i.e., the decomposition along the length of the prediction horizon, and provide preliminary numerical results on a practical application, the longitudinal control of an Airbus passenger aircraft.

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A randomized primal distributed algorithm for partitioned and big-data non-convex optimization

Notarnicola

Notarstefano

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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In this paper we consider a distributed optimization scenario in which the aggregate objective function to minimize is partitioned, big-data and possibly non-convex. Specifically, we focus on a setup in which the dimension of the decision variable depends on the network size as well as the number of local functions, but each local function handled by a node depends only on a (small) portion of the entire optimization variable. This problem set-up has been shown to appear in many interesting network application scenarios. As main paper contribution, we develop a simple, primal distributed algorithm to solve the optimization problem, based on a randomized descent approach, which works under asynchronous gossip communication. We prove that the proposed asynchronous algorithm is a proper, ad-hoc version of a coordinate descent method and thus converges to a stationary point. To show the effectiveness of the proposed algorithm, we also present numerical simulations on a nonconvex quadratic program, which confirm the theoretical results.

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Randomized dual proximal gradient for large-scale distributed optimization

Cited by 4 publications

References 22 publications

SVR-AMA: An Asynchronous Alternating Minimization Algorithm With Variance Reduction for Model Predictive Control Applications

SVR-AMA: An Asynchronous Alternating Minimization Algorithm With Variance Reduction for Model Predictive Control Applications

Asynchronous splitting design for Model Predictive Control

A randomized primal distributed algorithm for partitioned and big-data non-convex optimization

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